Find a recursive formula for $a_n$, $n ≥ 2$, in terms of $a_{n−1}$ and $a_{n−2}$, where $a_0 = 0, a_1 = 1$

Question

Find a recursive formula for $a_n$, $n\ge 2$, in terms of $a_{n-1}$ and $a_{n-2}$, where $a_0=0$, $a_1=1$, $a_2=-1$.

The power series is

$$\sum\frac{(-1)^{n-1}}{(n-1)!}$$

And can anyone help with mathjax, I can't seem to get a hang of it!